Drawing linear graphs：練習問題

What is the gradient of the line with the equation \(y = -3x + 5\)?

Find the equation of the line that is parallel to \(y = -2x + 5\) and passes through the point \((3, 4)\).

A line \(L_1\) passes through the points \((1, 2)\) and \((3, 8)\). A second line \(L_2\) is parallel to \(L_1\) and passes through the origin. What is the equation of line \(L_2\)?

The equation of a line is \(y = x + 4\). Which of the following tables correctly shows the value of \(y\) for \(x = -2, 0, 2\)?

The equation of a line is \(2y - 6x = 8\). Determine the y-intercept of this line.

When drawing the graph of the linear equation \(y = 3x - 7\), determine the coordinates of the point where the line crosses the \(y\)-axis.

To find the horizontal intercept for the graph of \(4x + 3y = 24\), determine the coordinates of the point where the line intersects the \(x\)-axis.

A straight line passes through the point \((2, -3)\) and is parallel to the line with equation \(y = 4x - 1\). Find the coordinates of the point where this line intersects the line defined by the equation \(x + y = 2\).

A linear graph passes through the points \(P(1, 4)\) and \(Q(3, 10)\).
(a) Calculate the gradient of the line passing through \(P\) and \(Q\).
(b) Find the coordinates of a third point \(R\) that lies on this line by using an \(x\)-coordinate of 5.
(c) State whether the line is increasing or decreasing as it moves from left to right.

A water storage tank initially contains 15 liters of water. A hose is turned on, adding water at a constant rate of 4 liters per minute.
(a) Write an equation for the volume of water, \(V\), in the tank after \(t\) minutes.
(b) Calculate the values of \(V\) for \(t = 0, 5, 10\).
(c) Using these values, determine the time taken for the volume to reach 55 liters.